{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Virtual Element for Poisson Equation in 2D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example is to show the rate of convergence of the linear virtual finite element approximation of the Poisson equation on the unit square:\n",
    "\n",
    "$$- \\Delta u = f \\; \\hbox{in } (0,1)^2$$\n",
    "\n",
    "for the following boundary conditions\n",
    "- Non-empty Dirichlet boundary condition: $u=g_D \\hbox{ on }\\Gamma_D, \\nabla u\\cdot n=g_N \\hbox{ on }\\Gamma_N.$\n",
    "\n",
    "\n",
    "**References**:\n",
    "- [Progamming of Linear Virtual Element Methods](http://www.math.uci.edu/~chenlong/226/vemCode.pdf)\n",
    "\n",
    "**Subroutines**:\n",
    "\n",
    "    - PoissonVEM\n",
    "    - squarePoissonVEM\n",
    "    \n",
    "The method is implemented in `PoissonVEM` subroutine and tested in `squarePoissonVEM`.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Polygon Meshes\n",
    "\n",
    "The polygonal mesh we used is generated by [*PolyMesher*](https://paulino.ce.gatech.edu/software.html) in MATLAB. The output contains a matrix named `Node` which represents the coordinates of vertices and a cell array named `Element` of which each cell records the vertices of each element with a counter-clockwise order. \n",
    "\n",
    "Polygon meshes used in this example are saved in data folder: `E16` to `E20014`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dFou8BKlJyEEigTEO37rV8wsMWaK3+8zeXiAc7p9PGwJaCrr75MkoF/Epik9R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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "load E64;\n",
    "showmeshpoly(Node,Element);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fj40wccNUiWwiQQqsQ8IqwrsbVYSsvPHGG9GWSwKrw+2+Bmuhhql9z32A82Qm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\nI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      "text/plain": [
       "<IPython.core.display.Image object>"
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   ],
   "source": [
    "u = @(p)cos(pi*p(:,1)).*cos(pi*p(:,2))-1;\n",
    "uI = u(Node);\n",
    "showsolutionpoly(Node,Element,uI);"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "## P1 Linear Virtual Element\n",
    "\n",
    "Let $\\mathcal T_h$ be a collection of partitions of domain $\\Omega$ into polygonal elements without self-intersecting boundary. The linear VEM space $V_h(E)$ for a polygon $E \\in \\mathcal T_h$ is defined as:\n",
    "\\begin{equation*}\\label{VEMspace2}\n",
    "V_h(E) := \\{ v \\in H^1(E): \\Delta v|_E = 0, v|_{\\partial E} \\text{ is continuous and piecewise linear}  \\}.\n",
    "\\end{equation*}\n",
    "Namely restricted to boundary edges of a polygon, the function is the standard linear Lagrange element. The interior is defined by the harmonic extension. \n",
    "Since a piecewise linear function will be uniquely determined by its value on vertices, $\\dim V_h(E)=n_E$, where $n_E$ is the number of vertices of $E$. \n",
    "\n",
    "The global virtual element space is defined as \n",
    "$$\n",
    "V_h = \\{v_h \\in H^1(\\Omega): v_h|_E \\in V_h(E)\\ \\text{ for all}\\ E \\in \\mathcal T_h\\}.\n",
    "$$\n",
    "\n",
    "Let $\\mathcal N(\\mathcal T_h)$ be the set of vertices of mesh $\\mathcal T_h$ and $N = |\\mathcal N(\\mathcal T_h)|$ be the number of vertices. \n",
    "We define the operator $\\operatorname{dof}$ (degree of freedom) from $V_h$ to $\\mathbb{R}^N$ as $\\operatorname{dof}_i(v_h) = v_h(\\boldsymbol  x_i)$, for a vertex $\\boldsymbol  x_i\\in \\mathcal N(\\mathcal T_h), i = 1,\\ldots, N$. The canonical basis $\\{\\phi_1,\\cdots, \\phi_{N}\\}$ of $V_h$ is chosen satisfying $\\operatorname{dof}_i(\\phi_j) = \\delta_{ij},  i,j = 1, \\cdots, N$.\n",
    "\n",
    "A basis function $\\phi_i$  is like the classical hat function of linear FE defined on triangular meshes. The difference is: for FEM functions, inside the element it is a linear polynomial while the VEM function is defined by the harmonic extension and function values inside the element is not explicitly known. The basis does not need to be known explicitly and this is the reason for the term *virtual* in VEM."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Assembeling\n",
    "\n",
    "To compute the stiffness matrix  $\\boldsymbol {A}_{ij} = (\\nabla \\phi_j, \\nabla \\phi_i)$ in the Galerkin method, we need to know the basis functions. Instead, the local stiffness matrix of the virtual element method is split into two parts:\n",
    "\\begin{align}\n",
    "(\\boldsymbol {A}_h^E)_{ij}:= (\\nabla \\Pi^\\nabla \\phi_i, \\nabla\\Pi^\\nabla \\phi_j)_{E} + \\sum_{r=1}^{n_E}{\\operatorname{dof}}_{r}((I- \\Pi^\\nabla) \\phi_i) \\, {\\operatorname{dof}}_r((I- \\Pi^\\nabla)\\phi_j),\n",
    "\\label{eq:stiffmatrix1}\n",
    "\\end{align}\n",
    "\n",
    "The operator $\\Pi^\\nabla : V_h(E) \\rightarrow  \\mathbb{P}_1(E)$ is an $H^1$ projection to $\\mathbb{P}_1(E)$ space:\n",
    "\\begin{equation}\\label{eq:projection}\n",
    "(\\nabla \\Pi^\\nabla v_h, \\nabla p)_{E} = (\\nabla v_h, \\nabla p)_{E} \\quad \\text{ for all } p \\in \\mathbb{P}_1(E).\n",
    "\\end{equation}\n",
    "\n",
    "The matrix representation of the projection is\n",
    "$$ \\boldsymbol {\\Pi}^\\nabla \\boldsymbol  v = \\boldsymbol  G^{-1} \\boldsymbol  B \\boldsymbol  v,$$\n",
    "where "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "The optimal rate of convergence of the H1-norm (1st order) and L2-norm\n",
    "(2nd order) is observed. The 2nd order convergent rate between two\n",
    "discrete functions $\\|\\nabla (u_I - u_h)\\|$ is known as superconvergence.\n",
    "\n",
    "MGCG converges uniformly in all cases."
   ]
  }
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